Application of Symbolic Computation in Nonlinear Differential-Difference Equations
A method is proposed to construct closed-form solutions of nonlinear differential-difference equations. For the variety of nonlinearities, this method only deals with such equations which are written in polynomials in function and its derivative. Some closed-form solutions of Hybrid lattice, Discre...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Wiley
2009-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2009/158142 |
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| _version_ | 1849685600363347968 |
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| author | Fuding Xie Zhen Wang Min Ji |
| author_facet | Fuding Xie Zhen Wang Min Ji |
| author_sort | Fuding Xie |
| collection | DOAJ |
| description | A method is proposed to construct closed-form solutions of nonlinear differential-difference equations. For the variety of nonlinearities, this method only deals with such equations which
are written in polynomials in function and its derivative. Some closed-form solutions of
Hybrid lattice, Discrete mKdV lattice, and modified Volterra lattice are obtained by using the
proposed method. The travelling wave solutions of nonlinear differential-difference equations
in polynomial in function tanh are included in these solutions. This implies that the proposed
method is more powerful than the one introduced by Baldwin et al. The results obtained in this
paper show the validity of the proposal. |
| format | Article |
| id | doaj-art-c48fb2121aec4a62b2193ad733c2ae82 |
| institution | DOAJ |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2009-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-c48fb2121aec4a62b2193ad733c2ae822025-08-20T03:23:03ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2009-01-01200910.1155/2009/158142158142Application of Symbolic Computation in Nonlinear Differential-Difference EquationsFuding Xie0Zhen Wang1Min Ji2Department of Computer Science, Liaoning Normal University, Liaoning, Dalian 116081, ChinaSchool of Physics and Electronic Technology, Liaoning Normal University, Liaoning, Dalian 116029, ChinaDepartment of Computer Science, Liaoning Normal University, Liaoning, Dalian 116081, ChinaA method is proposed to construct closed-form solutions of nonlinear differential-difference equations. For the variety of nonlinearities, this method only deals with such equations which are written in polynomials in function and its derivative. Some closed-form solutions of Hybrid lattice, Discrete mKdV lattice, and modified Volterra lattice are obtained by using the proposed method. The travelling wave solutions of nonlinear differential-difference equations in polynomial in function tanh are included in these solutions. This implies that the proposed method is more powerful than the one introduced by Baldwin et al. The results obtained in this paper show the validity of the proposal.http://dx.doi.org/10.1155/2009/158142 |
| spellingShingle | Fuding Xie Zhen Wang Min Ji Application of Symbolic Computation in Nonlinear Differential-Difference Equations Discrete Dynamics in Nature and Society |
| title | Application of Symbolic Computation in Nonlinear Differential-Difference Equations |
| title_full | Application of Symbolic Computation in Nonlinear Differential-Difference Equations |
| title_fullStr | Application of Symbolic Computation in Nonlinear Differential-Difference Equations |
| title_full_unstemmed | Application of Symbolic Computation in Nonlinear Differential-Difference Equations |
| title_short | Application of Symbolic Computation in Nonlinear Differential-Difference Equations |
| title_sort | application of symbolic computation in nonlinear differential difference equations |
| url | http://dx.doi.org/10.1155/2009/158142 |
| work_keys_str_mv | AT fudingxie applicationofsymboliccomputationinnonlineardifferentialdifferenceequations AT zhenwang applicationofsymboliccomputationinnonlineardifferentialdifferenceequations AT minji applicationofsymboliccomputationinnonlineardifferentialdifferenceequations |